MPs on the committee agreed before the summer recess that they would hold an inquiry into harmful online content. Although it will primarily focus on issues such as pornography, Whittingdale said that Twitter executives were likely to be summoned to give evidence, and that MPs would want to ask about its response to the rape and death threats directed against women.

Creasy and Criado-Perez have been the subject of particularly horrific abuse on Twitter in recent days, but their experience has highlighted a problem that many users of the site, especially women, have faced.

Although Twitter has been criticised for its tardy response to the threats directed at Creasy and Criado-Perez, Whittingdale said he did not know enough about the case to be able to comment on it. But the legal position was already clear, he said.

"The law is perfectly adequate. If someone posts a message on Twitter saying he's going to rape you, that is a criminal offence already. The challenge is how you identify people and prevent it," he said.

Whittingdale said it was "wholly unrealistic" to expect Twitter, or any other social media company, to employ people to monitor every single post.

But he said there were questions to be asked about how quickly companies such as Twitter responded to complaints, and how willing they are to co-operate with the police when people commit an offence online.

The cross-party committee, which has not met to discuss the recent complaints about Twitter, is expected to start taking evidence in October.

It will also take evidence from internet service providers, because a major focus of the inquiry will be the proposals to protect children from online pornography announced by David Cameron last week.